One day my boss asked if I would install this authentication app on my phone, so I would be able to push changes. I refused, stating that my phone is my private property. This resulted in quite a long conversation, with reassurances about security, etc. but I didn't budge. At one point they stated that my "argument wouldn't work" if it was on a company-provided phone. I completely agreed and said that would be fine, which seemed to surprise them.
I don't think it had even occurred to them that I was being honest: I didn't want to install random things on my phone. I wasn't making up some excuse to avoid being on call in the early hours.
(Of course, I also wasn't going to suggest a way to end up on call in the early hours!)